Self Adjointness and Normality of Hankel Operators

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M . Restricting to H and multiplying on the left by P gives H PJM f2 .

Clearly, H .

4.2 Hankel Operators of Finite Rank

There are many Hankel operators of nite rank. For example, if the function in L has only a nite number of nonzero Fourier coefficients in positions of negative index, then clearly H has nite rank. In fact, in those cases, the standard matrix representation of H has only a nite number of entries other than zero. There are also nite-rank Hankel operators whose standard matrices con- tain an innite number of entries other than zero. As will be shown, the Hankel operators of rank 1 arise from the kernel functions for H2. We will nd it useful to have notation for the function obtained from a...

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